{"id":"https://openalex.org/W2143106608","doi":"https://doi.org/10.1109/tcsi.2008.2008286","title":"Optimized Waveform Relaxation Methods for Longitudinal Partitioning of Transmission Lines","display_name":"Optimized Waveform Relaxation Methods for Longitudinal Partitioning of Transmission Lines","publication_year":2008,"publication_date":"2008-11-06","ids":{"openalex":"https://openalex.org/W2143106608","doi":"https://doi.org/10.1109/tcsi.2008.2008286","mag":"2143106608"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2008.2008286","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2008.2008286","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://archive-ouverte.unige.ch/unige:6265","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033641370","display_name":"Mohammad Al-Khaleel","orcid":"https://orcid.org/0000-0001-6266-373X"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]},{"id":"https://openalex.org/I85507684","display_name":"Yarmouk University","ror":"https://ror.org/004mbaj56","country_code":"JO","type":"education","lineage":["https://openalex.org/I85507684"]}],"countries":["CA","JO"],"is_corresponding":false,"raw_author_name":"M. Al-Khaleel","raw_affiliation_strings":["Department of Mathematics and Statistics, McGill University, Montreal, QUE, Canada","Department of Mathematics, Yarmauk University, Irbid, Jordan","Dept. of Math. & Stat., McGill Univ., Montreal, QC, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, McGill University, Montreal, QUE, Canada","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"Department of Mathematics, Yarmauk University, Irbid, Jordan","institution_ids":["https://openalex.org/I85507684"]},{"raw_affiliation_string":"Dept. of Math. & Stat., McGill Univ., Montreal, QC, Canada","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026900188","display_name":"A.E. Ruchli","orcid":null},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]},{"id":"https://openalex.org/I4210114115","display_name":"IBM Research - Thomas J. Watson Research Center","ror":"https://ror.org/0265w5591","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A.E. Ruchli","raw_affiliation_strings":["IBM Research Division, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA","Res. Div., T.J. Watson Res. Center, IBM, Yorktown Heights, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM Research Division, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA","institution_ids":["https://openalex.org/I4210114115"]},{"raw_affiliation_string":"Res. Div., T.J. Watson Res. Center, IBM, Yorktown Heights, NY, USA","institution_ids":["https://openalex.org/I1341412227"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089456729","display_name":"Martin J. Gander","orcid":"https://orcid.org/0000-0001-8450-9223"},"institutions":[{"id":"https://openalex.org/I114457229","display_name":"University of Geneva","ror":"https://ror.org/01swzsf04","country_code":"CH","type":"education","lineage":["https://openalex.org/I114457229"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"M.J. Gander","raw_affiliation_strings":["Department of Mathematics, University of Geneva, Geneva, Switzerland","Dept. of Math., Univ. of Geneva, Geneva, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Geneva, Geneva, Switzerland","institution_ids":["https://openalex.org/I114457229"]},{"raw_affiliation_string":"Dept. of Math., Univ. of Geneva, Geneva, Switzerland","institution_ids":["https://openalex.org/I114457229"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6959,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.85399156,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"56","issue":"8","first_page":"1732","last_page":"1743"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11444","display_name":"Electromagnetic Compatibility and Noise Suppression","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10363","display_name":"Low-power high-performance VLSI design","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/waveform","display_name":"Waveform","score":0.7322157621383667},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6807117462158203},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6356631517410278},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6229793429374695},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.6101719737052917},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6022061705589294},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.5552911162376404},{"id":"https://openalex.org/keywords/transmission-line","display_name":"Transmission line","score":0.5175401568412781},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5174906253814697},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.48537909984588623},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4678756892681122},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4647101163864136},{"id":"https://openalex.org/keywords/spice","display_name":"Spice","score":0.4349541664123535},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4273185431957245},{"id":"https://openalex.org/keywords/electric-power-transmission","display_name":"Electric power transmission","score":0.4268338680267334},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4064652919769287},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37803810834884644},{"id":"https://openalex.org/keywords/electronic-engineering","display_name":"Electronic engineering","score":0.34357982873916626},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31713810563087463},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28771859407424927},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.24563774466514587},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23555031418800354},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.10371208190917969},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.10200309753417969},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.09804177284240723}],"concepts":[{"id":"https://openalex.org/C197424946","wikidata":"https://www.wikidata.org/wiki/Q1165717","display_name":"Waveform","level":3,"score":0.7322157621383667},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6807117462158203},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6356631517410278},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6229793429374695},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.6101719737052917},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6022061705589294},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.5552911162376404},{"id":"https://openalex.org/C33441834","wikidata":"https://www.wikidata.org/wiki/Q693004","display_name":"Transmission line","level":2,"score":0.5175401568412781},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5174906253814697},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.48537909984588623},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4678756892681122},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4647101163864136},{"id":"https://openalex.org/C2780077345","wikidata":"https://www.wikidata.org/wiki/Q16891888","display_name":"Spice","level":2,"score":0.4349541664123535},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4273185431957245},{"id":"https://openalex.org/C140311924","wikidata":"https://www.wikidata.org/wiki/Q200928","display_name":"Electric power transmission","level":2,"score":0.4268338680267334},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4064652919769287},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37803810834884644},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.34357982873916626},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31713810563087463},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28771859407424927},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.24563774466514587},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23555031418800354},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.10371208190917969},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.10200309753417969},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.09804177284240723},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tcsi.2008.2008286","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2008.2008286","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","raw_type":"journal-article"},{"id":"pmh:oai:unige.ch:unige:6265","is_oa":true,"landing_page_url":"https://archive-ouverte.unige.ch/unige:6265","pdf_url":null,"source":{"id":"https://openalex.org/S4306402259","display_name":"Archive ouverte UNIGE (University of Geneva)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114457229","host_organization_name":"University of Geneva","host_organization_lineage":["https://openalex.org/I114457229"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"ISSN: 1549-8328","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.156.8260","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.156.8260","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.unige.ch/~gander/Preprints/PaperChappa.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:unige.ch:unige:6265","is_oa":true,"landing_page_url":"https://archive-ouverte.unige.ch/unige:6265","pdf_url":null,"source":{"id":"https://openalex.org/S4306402259","display_name":"Archive ouverte UNIGE (University of Geneva)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114457229","host_organization_name":"University of Geneva","host_organization_lineage":["https://openalex.org/I114457229"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"ISSN: 1549-8328","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1509997287","https://openalex.org/W1531077154","https://openalex.org/W1532580938","https://openalex.org/W1535908348","https://openalex.org/W1575111222","https://openalex.org/W1965273420","https://openalex.org/W1998789711","https://openalex.org/W1999197715","https://openalex.org/W2004542458","https://openalex.org/W2007510482","https://openalex.org/W2025377524","https://openalex.org/W2036597275","https://openalex.org/W2041146028","https://openalex.org/W2049090480","https://openalex.org/W2051545363","https://openalex.org/W2078641415","https://openalex.org/W2099101457","https://openalex.org/W2099693095","https://openalex.org/W2101531703","https://openalex.org/W2113320423","https://openalex.org/W2123153035","https://openalex.org/W2138337420","https://openalex.org/W2147882918","https://openalex.org/W2148615197","https://openalex.org/W2149649731","https://openalex.org/W2163356590","https://openalex.org/W2165213681","https://openalex.org/W4213104200","https://openalex.org/W4231111020","https://openalex.org/W4233031217"],"related_works":["https://openalex.org/W3082668976","https://openalex.org/W2517973022","https://openalex.org/W1543121148","https://openalex.org/W1580703421","https://openalex.org/W2618518959","https://openalex.org/W2231364979","https://openalex.org/W4295745414","https://openalex.org/W4382202915","https://openalex.org/W4288093367","https://openalex.org/W2489516236"],"abstract_inverted_index":{"Waveform":[0],"relaxation":[1],"(WR)":[2],"is":[3,20,58,101,122],"a":[4,90],"technique":[5],"that":[6,130],"can":[7],"be":[8],"used":[9,37],"to":[10,112,126],"solve":[11],"large":[12],"systems":[13],"of":[14,27,41,56,61,89,120,148],"ordinary":[15],"differential":[16,48],"equations":[17],"(ODEs).":[18],"It":[19],"particularly":[21],"suitable":[22],"for":[23,38,45,143],"the":[24,39,54,59,96,108,127],"parallel":[25],"solution":[26,40],"ODEs":[28],"with":[29,63,139],"multiple":[30],"time":[31,70],"scales":[32],"and":[33,44,67,104,150],"has":[34],"successfully":[35],"been":[36],"electronic":[42],"circuits":[43,82],"solving":[46],"partial":[47],"equations.":[49],"The":[50],"main":[51],"issue":[52],"limiting":[53],"utility":[55],"WR":[57,115],"class":[60],"problems":[62],"strong":[64,128],"subsystem-to-subsystem":[65],"couplings":[66],"long":[68],"analysis":[69],"intervals":[71],"resulting":[72],"in":[73,107],"nonuniform":[74],"slow":[75],"convergence.":[76],"Here,":[77],"we":[78,135],"consider":[79],"transmission-line":[80],"(TL)":[81],"since":[83],"they":[84],"represent":[85],"an":[86,137],"important":[87],"part":[88],"Spice-type":[91],"circuit":[92],"solver.":[93],"For":[94],"TLs,":[95],"coupling":[97,129],"between":[98],"different":[99],"lines":[100],"relatively":[102],"weak,":[103],"thus,":[105],"partitioning":[106,119,147],"transverse":[109],"direction":[110],"leads":[111],"very":[113,123],"fast":[114],"algorithms.":[116],"However,":[117],"longitudinal":[118,146],"TLs":[121,149],"challenging":[124],"due":[125],"results.":[131],"In":[132],"this":[133],"paper,":[134],"propose":[136],"approach":[138],"improved":[140],"convergence":[141],"properties":[142],"strongly":[144,153],"coupled":[145,154],"other":[151],"similarly":[152],"circuits.":[155]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":6}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}